NCERT Exemplar Class 12th Math Problem Solution PDF

The NCERT Exemplar Class 12 Maths book is a powerful resource for practicing advanced problem-solving and scoring high in exams. While NCERT builds the basics, Exemplar helps you apply concepts in deeper and more complex situations.

Its questions improve analytical thinking, logical reasoning, and accuracy. These are the skills essential for CBSE boards and competitive exams like JEE. Teachers recommend it for practicing higher-order thinking (HOTS) questions now common in exams.

Maths Class 12 NCERT Exemplar  PDF

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Overview NCERT Exemplar Class 12 Maths 

The NCERT Exemplar Class 12 Maths book is a supplementary practice resource developed by NCERT to help students deepen their conceptual clarity and application skills.

As per the latest CBSE curriculum, this book focuses on advanced problem-solving and real-life application of mathematical concepts. It is especially useful for students aiming for top scores and preparing for competitive exams.

Key Highlights: NCERT Class 12 Maths Exemplar

• Covers all chapters from the NCERT Class 12 Mathematics syllabus
• Includes MCQs, very short answer, short answer, and long answer questions
• Focuses on application-based and concept-driven problems
• Improves logical reasoning and analytical thinking
• Recommended by teachers for board exam preparation and beyond

Chapter-wise Exemplar Questions

The NCERT Class 12 Maths Exemplar includes a wide variety of challenging questions that test deep understanding and application skills.

Chapter 1: Relations and Functions

Q: Which of the following functions is one-one?

A) f(x) = x²
B) f(x) = x³
C) f(x) = |x|
D) f(x) = sinx

Answer: B
Explanation: Only x³ is strictly increasing and hence one-one.

Chapter 2: Inverse Trigonometric Functions

Q: The value of sin⁻¹(1/2) is:

A) π/6
B) π/4
C) π/3
D) π/2

Answer: A
Explanation: sin(π/6) = 1/2

Chapter 3: Matrices

Q: If A is a 2×2 identity matrix, then A² =

A) A
B) 2A
C) 0
D) I

Answer: A
Explanation: Identity matrix squared remains the same.

Chapter 4: Determinants

Q: If determinant of a matrix is zero, then the matrix is:

A) Identity
B) Singular
C) Diagonal
D) Symmetric

Answer: B
Explanation: Zero determinant implies a singular matrix.

Chapter 5: Continuity and Differentiability

Q: If f(x) is differentiable, then it is:

A) Discontinuous
B) Continuous
C) Periodic
D) Constant

Answer: B
Explanation: Differentiability implies continuity.

Chapter 6: Applications of Derivatives

Q: Maximum value occurs where derivative is:

A) Positive
B) Negative
C) Zero
D) Undefined

Answer: C
Explanation: At maxima, derivative equals zero.

Chapter 7: Integrals

Q: ∫ dx =

A) x
B) x + C
C) 1
D) 0

Answer: B
Explanation: Integral of 1 is x + constant

Chapter 8: Applications of Integrals

Q: Area under a curve is calculated using:

A) Derivatives
B) Integrals
C) Limits
D) Matrices

Answer: B
Explanation: Integration gives area under curve.

Chapter 9: Differential Equations

Q: Order of differential equation is:

A) Highest power
B) Highest derivative
C) Degree
D) Constant

Answer: B
Explanation: Order is the highest derivative present.

Chapter 10: Vector Algebra

Q: Dot product of perpendicular vectors is:

A) 1
B) −1
C) 0
D) Undefined

Answer: C
Explanation: Cos 90° = 0

Chapter 11: 3D Geometry

Q: Distance between (1,2,3) and (4,6,3):

A) 5
B) √5
C) 3
D) 7

Answer: A
Explanation: Distance = √[(3)²+(4)²] = 5

Chapter 12: Linear Programming

Q: Objective function is used to:

A) Define constraints
B) Optimize value
C) Draw graph
D) Solve equations

Answer: B
Explanation: It maximizes or minimizes value.

Chapter 13: Probability

Q: Probability of an event lies between:

A) −1 and 1
B) 0 and 1
C) 0 and ∞
D) −∞ and ∞

Answer: B
Explanation: Probability ranges from 0 to 1

Latest Updates in NCERT Exemplar Class 12 Maths

With evolving exam patterns and a stronger focus on application-based learning, NCERT Exemplar has become even more relevant for Class 12 Maths preparation.

Alignment with CBSE competency-based pattern

• Questions reflect the latest CBSE shift towards application and competency-based assessment.
• More emphasis on concept application instead of direct formula-based answers.
• Helps students adapt to case-based and real-life problem formats.

Increased focus on HOTS and case-based questions

• Strong presence of HOTS (Higher Order Thinking Skills) questions.
• Includes multi-step and situation-based problems to test deeper understanding.
• Encourages logical reasoning rather than rote learning.

Important for board exam preparation

• Matches the evolving difficulty level of CBSE board exams.
• Helps improve accuracy, speed, and exam confidence.
• Acts as a reliable source for last-mile revision and advanced practice.

NCERT Exemplar Maths vs NCERT Textbook

The difference down below depicts how NCERT Textbooks for Maths Class 12 are different from Exemplar. 

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Benefits of NCERT Maths Exemplar for Class 12

NCERT Maths Exemplar is designed to take your preparation beyond basic problem-solving. It strengthens your concepts while training you to handle tricky, exam-level questions with confidence.

• Strengthens application of concepts
  Helps you apply formulas and concepts in new and unfamiliar situations, not just standard textbook problems.
• Improves problem-solving approach
  Trains you to think step-by-step and choose the right method instead of guessing or memorizing patterns.
• Prepares you for HOTS questions
  Includes higher-order thinking questions that are increasingly asked in CBSE board exams.
• Boosts accuracy and reduces errors
  Regular practice improves calculation skills and minimizes common mistakes in exams.
• Builds exam-level confidence
  Exposure to moderate and difficult questions makes actual exam questions feel more manageable.
• Enhances logical and analytical thinking
  Encourages deeper understanding and reasoning, especially in algebra, calculus, and probability.
• Supports competitive exam preparation
  Forms a strong base for exams like JEE by improving conceptual clarity and speed.
• Acts as an effective revision tool
  Revisiting Exemplar questions helps reinforce key concepts quickly before exams.

How to Solve Class 12 Maths Problems 

Class 12 Maths problems are less about memorizing formulas and more about how you approach them mentally. The right mindset can turn even the toughest questions into manageable steps and help you stay calm under pressure.

1. Focus on knowing the “why” behind concepts, not just formulas

2. Treat difficult questions as puzzles, not obstacles

3. Break problems into smaller steps instead of trying to solve everything at once

4. Accept that getting stuck is part of the learning process

5. Avoid rushing. Accuracy matters more than speed in advanced questions

6. Learn to analyze mistakes instead of getting frustrated by them

7. Stay consistent; problem-solving skills build over time, not overnight

FAQs

Q1. What is NCERT Exemplar for Class 12 Maths?

Ans. It is a supplementary book with advanced and application-based questions to improve conceptual understanding.

Q2. Are NCERT Exemplar questions important for Class 12 exams?

Ans. Yes, they help in practicing higher-order thinking questions and improving performance.

Q3. Is the NCERT Class 12 Maths Exemplar available chapter-wise?

Ans. Yes, it is available as both full-book and chapter-wise PDFs.

Q4. Are exemplar questions tougher than NCERT textbook questions?

Ans. Yes, they are more challenging and concept-based.

Q5. When should students solve the NCERT Exemplar?

Ans. After completing NCERT textbook to strengthen concepts and practice advanced problems.